Show img in coordinate system and perform transformations

I want to show my image in xy-coordinate system, Now I have img and I can read it without any problem

I = imread('img.png');
size(I); % 16 x 15
imshow(I);

Now the img shows like this,

Now I wanted it to be shown like a graph with proper x,y coordinates.

For example the size of img is 16x15 and corners of the img by default should be as

Bottom Left: (0,0)

Bottom Right: (16, 0)

Top Left: (0, 15)

Top Right: (16, 15)

Now, comes the real part. img is displayed in coordinate system with these points.

Now I want to perform transformations, I will try to explain it in detail with example

For example I am given a scenerio

Apply Shear of factor 2 in y direction. Now first we find the Standard matrix and then get new coordinates

The 2nd is the Standard matrix while thrd is the unit vector (img in our case) and fourth is the transformed vector.

I want to do this with the img, using Standard matrix getting new coordinates and displaying img accordingly. I can show it mathematically in detail.

Now the standard matrix will be

T = [1 0

2 1] % from the above img

Now new coordinates would be

Bottom Left = T * [0; 0] = [0; 0]

Bottom Right: (16, 0) = T * [16; 0] = [16; 32]

Top Left: (0, 15) = T * [0; 15] = [0; 15]

Top Right: (16, 15) = T * [16; 15] = [16; 47]

Now, I have the new coordinates, I want the img to be displayed according to the new coordinates. This is the end goal I want to acheive. I would have to apply different Standard matrixes at different ocations, so do not want the solution to work only for shear factor.

[Catalytic]

You asked essentially the same question and got essentially the same answers in this earlier post. Why did you abandon it?

[Farhan]

I tried messing with that but could not get what I wanted, I thought I might have done question wrong. So decided to make it more clear.Now I have understood what to do. Thanks.

Answer 1

[Matt J]

I=flipud(imread('peppers.png'));

T = [1  0
     2  1]; T(3,3)=1;

[Iw,R]=imwarp(I, affine2d(T'));

h=imshow(Iw);
    axis on xy;
    set(h,'XData',R.XWorldLimits,'YData',R.YWorldLimits);
    set(gca,'XLim',R.XWorldLimits,'YLim',R.YWorldLimits);

[Farhan]

This is correct for the above transormation, though for others it is giving inverse.

For example

For this transformation (k=2) I get

Another that I tested is

The reflection one. Now the image is reflected though it remains above the axis line.

I know it is my task but I have been strugling for 3 to 4 days and didn't find any solution

[Matt J]

I=imread('peppers.png');
I=flipud(I);

T{1} = [1  0
        1.2 1]; 

T{2} = diag([1,1.5]); 

T{3} =diag([1,-1]);


for i=1:numel(T)
    figure(i)
    
    Ti=T{i}, 
    Ti(3,3)=1;

    [Iw,R]=imwarp(I, affine2d(Ti'));


    h=imshow(Iw);
    axis on xy;
    set(h,'XData',R.XWorldLimits,'YData',R.YWorldLimits);
    set(gca,'XLim',R.XWorldLimits,'YLim',R.YWorldLimits);

end

Ti = 2×2

1.0000 0 1.2000 1.0000

Ti = 2×2

1.0000 0 0 1.5000

Ti = 2×2

1 0 0 -1

[Farhan]

The axis is set on after the img is shown, I think this is causing the wrong xy position in reflection case, because the img should be below the x-axis line. Similar problem in reflection against y-axis

Also, can you explain this a bit so I can try it my self too

[Matt J]

The axis is set on after the img is shown, I think this is causing the wrong xy position in reflection case

I fixed it.

Also, can you explain this a bit so I can try it my self too

I would need specific questions. imwarp does all the work, so you should definitely read that doc page thoroughly.

Answer 2

[Image Analyst]

"I want to show my image in xy-coordinate system" <== Did you try calling axis xy?

axis xy

Call it after you call imshow.